Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

STATISTICS FOR BUSINESS

NBS-5108B

1. Question (Total 16 marks)

This question uses the dataset gym2.sav that captures data from 93 members of a gym in relation to their reason for visiting the gym, the frequency of their visits to the gym and the total time they spent there, their gender, and whether they visit the gym with company.

The dataset contains 6 variables:

Reason: The reason for which a member visits the gym

Accompanied: Whether a member visits the gym with company or not

Frequency: How many times a week a member visits the gym

Gender: The gender of the gym member

TotalTime: The total time a member spends in the gym during a visit in minutes

TotalTimeGroup: The “total time a member spends in the gym” group during a visit

a) Use SPSS to produce point estimates of the amount of time gym members spent on average in the gym during a visit across the different “reason for visit” groups: “relaxation”, “fitness”, “lose weight”, and “other”. Comment on your findings. Include your SPSS output in your answer.

[5 marks]

The gym manager believes that members who visit the gym to lose weight spent on average 90mins in the gym.

a) Which statistical test would you use to assess the manager’s belief? Explain why this test is appropriate. Provide the null and alternative hypothesis for the test. Define any symbols you use. Detail any assumptions you make.   

[5 marks] 

Use SPSS to perform this test.

b) Do the data provide significant evidence to support the manager’s belief at the 5% significance level? Write down your results and conclusions providing statistical evidence. Include any SPSS output tables you might refer to in your answer.

[6 marks]

2. Question (Total 8 marks)

This question continues to use the dataset gym2.sav.

The gym manager wishes to further explore the collected data and would like to find out whether there is an association between the frequency of visits to the gym by a member and the total time-group-spent in the gym during a visit.

Use SPSS to assess the association between the frequency of visits to the gym by a member and the total time-group-spent in the gym during a visit. Write down your results. Include any SPSS output table you might refer to in your answer.

[8 marks] 

3. Question (Total 41 marks) 

Introduction to the Data File

There has been concern recently about whether the intake of salt and caffeine affects blood pressure of people over the age of 50.  Blood pressure is measured in two ways: systolic (when the heart is pumping out) and diastolic (when the heart is filling with blood).  The units of blood pressure is mm Hg (millimetres of mercury).  A healthy systolic blood pressure can be anywhere between 90 and 130 mm Hg.  Hypertension is a condition where the blood pressure is high, measuring between 140 and 180 mm Hg.

A small study of 30 randomly selected people measured their systolic blood pressure, age, daily salt intake (in grams), body mass (in kilograms) and if they drank more than 4 cups of coffee a day.  The results are contained in the SPSS data file Bloodpressure.sav.  

The dataset contains 5 variables:

age: the age of the patient (years).

pressure: the systolic blood pressure of the patient (mm Hg).

coffee: whether the patient consumes more than 4 cups of coffee a day or not.

mass: the mass of the patient (kg).

salt: the amount of salt the patient consumes daily (g).

Provide relevant SPSS outputs with your answers where applicable.

a) Use SPSS to assess the sample and population correlation between the patient’s blood pressure (mm Hg) and age (years).  

[6 marks]

c) Write down the assumed multiple linear regression model you might use to predict the mean blood pressure (mm Hg) from the patient’s age (years), coffee consumption, body mass (kg), and salt consumption (g).  Define any symbols you use and assumptions you make in developing your model.

[7 marks] 

Use SPSS to run this model.

d) Why would you use the adjusted coefficient of determination in this analysis?  Interpret the value you have.

[4 marks] 

e) Following the four-step testing procedure, interpret the ANOVA test at the 1% level.

[7 marks]

f) Write down your estimated model and your estimate of .

[4 marks]

g) Interpret the value of the coefficient for the coffee variable.

[3 marks] 

h) Predict the mean blood pressure for someone aged 55 with a body mass of 85 kg who consumes 5 grams of salt and six cups of coffee per day.

[2 marks] 

i) What role do the t-tests play in the multiple regression analysis? Write down the general hypotheses for these tests.  Use the specific p-values for each coefficient and comment on the significance of each independent variable at the 5% significance model

[8 marks] 

4. Question (25 marks) 

One of the products of a plastic toy manufacturer is small plastic figurines to place as surprise gifts inside hollow chocolate eggs. As part of the quality control process, the manufacturer samples the figurines and checks their weight (measured in grams). Here are the data of 14 random samples, each of four figurines.

Sample 1

Sample 2

Sample 3

Sample 4

Sample 5

Sample 6

Sample 7

4.1

3.6

4.0

4.6

3.9

5.1

4.6

5.2

4.3

4.8

4.8

3.8

4.7

4.4

3.9

3.9

5.1

4.7

4.6

4.8

4.0

5.0

4.6

5.3

4.7

4.9

4.3

4.5

 

 

 

 

 

 

 

Sample 8

Sample 9

Sample 10

Sample 11

Sample 12

Sample 13

Sample 14

4.2

3.50

4.9

3.6

5.1

3.9

5.1

5.3

4.20

4.6

3.5

4.7

4.8

4.3

4.0

3.80

4.6

4.3

4.8

4.6

5.0

5.1

4.50

4.8

5.0

4.3

5.2

5.2

a) Calculate the sample means and the sample ranges for the 14 samples.

[3.5 marks] 

j) Calculate the mean of the 14 sample means and the mean of the 14 sample ranges.

[4 marks]

k) Using the table provided at the end of the question, define the constants required to calculate the control limits to construct an  chart and an R chart.

         [3.5 marks] 

l) Calculate the control limits for an  chart and the control limits for an R chart. Define the centrelines for both control charts.

[8 marks]

m) Enter the data in SPSS and produce an  chart and an  chart. Comment on the two control charts. Provide your SPSS outputs.

         [6 marks] 

Sample size, n

A2

D3

D4

2

1.88

0

3.267

3

1.023

0

2.574

4

0.729

0

2.282

5

0.577

0

2.114

6

0.483

0

2.004

7

0.419

0.076

1.924

8

0.373

0.136

1.864

9

0.337

0.184

1.816

10

0.308

0.223

1.777

11

0.285

0.256

1.744

12

0.266

0.283

1.717

13

0.249

0.307

1.693

14

0.235

0.328

1.672

15

0.223

0.347

1.653

16

0.212

0.363

1.637

17

0.203

0.378

1.622

18

0.194

0.391

1.608

19

0.187

0.403

1.597

20

0.18

0.415

1.585

21

0.173

0.425

1.575

22

0.167

0.434

1.566

23

0.162

0.443

1.557

24

0.157

0.451

1.548

25

0.153

0.459

1.541

5. Question (10 marks) 

A manufacturer of luxury leather goods produces leather accessories for high end department stores, including handbags, belts, and wallets. As they target the upper-end of the leather accessories market, goods produced should meet very high specifications. As part of the quality control process, the manufacturer samples 6 wallets from every production run and checks that they meet the specifications. Here are the data of the number of wallets found in noncompliance over 10 production runs.   

Sample

number of wallets in noncompliance

1

0

2

1

3

2

4

3

5

4

6

5

7

3

8

2

9

0

10

0

a) Calculate the noncompliance proportion for each sample.

         [1 mark] 

n) Calculate the mean noncompliance proportion across the 10 samples.

[2 mark]

o) Calculate the control limits (UCL and LCL) and define the centreline for a  control chart.

         [4 marks]

p) Enter the data in SPSS and produce a  chart. Comment on the control chart. Provide your SPSS output.

         [3 marks]